Question

Cost of 5 pencils and 7pens is Rs 95 .Also as of 3 pencils and 5 pans is Rs .65.Find the cost of a pen and a pencil . class 10​

Answer 1

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Given :-

• Cost of 5 pencils and 7 pens is Rs 95.
• Cost of 3 pencils and 5 pens is Rs 65.

To Find :-

• The cost of a pen and a pencil.

Solution :-

Let the cost of 1 pencil be 'x' Rs and Cost of 1 pen be 'y' Rs.

So, according to the question :

Cost of 5 pencils and 7 pens is Rs 95

• 5x + 7y = 95 ..eq 1

Cost of 3 pencils and 5 pens is Rs 65.

• 3x + 5y = 65 ..eq 2

BY ELIMINATION METHOD :

⟼ Multiplying 3 on both sides of eq 1 :

3 (5x + 7y) = 3(95)

15x + 21y = 285 ..eq 3

⟼ Multiplying 5 on both sides of eq 2 :

5 (3x + 5y) = 5(65)

15x + 25y = 325 ..eq 4

⟼ By subracting eq 3 from eq 4 :

(15x + 25y) - (15x + 21y) = 325 - 285

25y - 21y = 40

4y = 40

• y = 10

⟼ By substituting the value of y in eq 1 :

5x + 7(10) = 95

5x + 70 = 95

5x = 25

• x = 5

Therefore,

Cost of one pencil = x = Rs. 5

Cost of one pen = y = Rs. 10

@SweetestBitter